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    Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer

    2018, Vol. 14, no. 1, pp.  69-79

    Author(s): Privalova V., Prosviryakov E. Y.

    This paper presents an exact solution to the Oberbeck – Boussinesq system which describes the flow of a viscous incompressible fluid in a plane channel heated by a linear point source. The exact solutions obtained generalize the isothermal Couette flow and the convective motions of Birikh – Ostroumov. A characteristic feature of the proposed class of exact solutions is that they integrate the horizontal gradient of the hydrodynamic fields. An analysis of the solutions obtained is presented and thus a criterion is obtained which explains the existence of countercurrents moving in a nonisothermal viscous incompressible fluid.



    Keywords: Couette flow, Birikh – Ostroumova flow, planar Rayleigh – Benard convection, quadratic heating, exact solution, counterflow
    Citation: Privalova V., Prosviryakov E. Y., Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  69-79
    DOI:10.20537/nd1801007


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